The big idea: A planet stays in orbit because the Sun's gravity constantly pulls it inward.
That inward pull bends the planet's path into a closed orbit instead of letting it fly off in a straight line.
Kepler's three laws describe the shape, speed and timing of these orbits.
Gravity pulls inward (field lines point to the centre). This inward pull is what keeps a planet circling the Sun instead of flying off in a straight line.
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Kepler's three laws in plain words: 1st law: orbits are ellipses (slightly squashed circles), with the Sun at one focus.
2nd law: a planet moves faster when it is closer to the Sun and slower when it is farther away.
3rd law: the period T and the orbit radius r are linked — bigger orbits take longer.
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Kepler's third law links how long an orbit takes to how big it is. The period squared is proportional to the orbit radius cubed:
- orbital period — time for one full orbit (s)
- orbital radius — distance from the central body (m)
- universal gravitational constant (6.67 × 10⁻¹¹ N m² kg⁻²)
- mass of the central body being orbited (kg)
Where it comes from (both pieces ARE given): Gravity provides the centripetal pull, so the given field equation g = GM ÷ r² equals the given centripetal acceleration a = 4π²r ÷ T².
Setting them equal and rearranging gives T² = 4π²r³ ÷ (GM).
You rarely need the constants: the useful idea is just T² is proportional to r³.
- gravitational field strength (N kg⁻¹)
- gravitational force on the orbiting mass (N)
- mass of the orbiting body (kg)
- mass of the central body (kg)
- distance from the centre of the central body (m)
Comparing two orbits — the shortcut: Because T² ÷ r³ is the same for every body orbiting the same central mass, two orbits A and B obey:
TA² ÷ rA³ = TB² ÷ rB³
The constant 4π² ÷ (GM) cancels, so you never need G or M — just the ratios.
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Planet A orbits a star with period 2.0 years at radius r. Planet B orbits the same star at radius 4r. Find the orbital period of planet B.
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How this is tested — Kepler's laws are the tool the orbits questions are built on:
Paper 1A
- A quick MCQ — recognise that T² ∝ r³.
- Or pick the right exponents in Tⁿ ∝ rᵐ.
Paper 2
- Calculate a ratio of two periods from their radii (or radii from periods) using T² ÷ r³ shared between the two orbits.
- State Kepler's first law, or explain the speed change from the second.
The classic trap: Forgetting the powers — it is T squared and r cubed, not T and r.
Ratio method (no G or M needed): For two bodies round the same central mass:
TA² ÷ rA³ = TB² ÷ rB³
Rearrange for whichever quantity is missing. The constant cancels, so you never need the star's mass.
Two planets, X and Y, orbit the same star. Planet X has an orbital period of 1.0 year; planet Y has a period of 8.0 years. Find the ratio of their orbital radii (planet Y to planet X).
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State Kepler's first law of planetary motion.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.